Math word problems can be very difficult, especially for grade school children. A recent study investigated a combination of techniques for teaching grade school children to master such problems: tutoring (none, small group, one-on-one) and in-class instruction (traditional, hot math). The hot-math program teaches students to recognize types or categories of problems so that they can generalize skills from one problem to another. The following data are similar to the results obtained in the study. The dependent variable is a math test score for each student after 16 weeks in the study. Test the effectiveness of these two techniques, individually and in combination, using a two-factor ANOVA with ?=0.05. ? Tutoring none small group one-on-one Hot math instruction M=3 T = 15 SS = 18 M=6 T = 30 SS = 28 M=9 T = 45 SS = 26 Traditional instruction M=1 T=5 SS = 8 M=4 T = 20 SS = 20 M=1 T=5 SS = 20 a. State the hypotheses for each of the 3 separate tests in this two-factor ANOVA. b. Calculate degrees of freedom and identify the critical region for each of the 3 tests. c. Calculate the 3 F-ratios and show all relevant values in a summary table d Draw a graph to show math test scores for these two factors; by eye, interpret the interaction e. State your conclusion for each of the 3 tests (statistical & in real terms)
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